The Unreasonable Effectiveness of Operations Research

On Monday, I had
pointed to visibility dilemma bedeviling the profession of operations
research (OR) thus:

... mentions of OR in the popular press are few and far between. Worse yet,
popular media articles covering OR manage to avoid mentioning OR entirely!

On Tuesday, Steve Lohr's New York Times blog post, titled "Software
Progress Beats Moore's Law," appeared. It mentioned "Martin Grotschel, a
German scientist and mathematician." Over the 20-odd years that I've known
Martin Grotschel, we have not discussed his primary professional affiliation.
Nevertheless, even a cursory survey of his research
interests will suggest that Martin is at least as much an operations
researcher as he is a mathematician or an omnibus "scientist." Martin's OR
expertise is entirely missing in Lohr's story. (The bias that "pure" mathematics
is better, or harder, or more meaningful, than applied mathematics isn't
universal, but it is pervasive. OR is application-focused. Lest I be slotted as
a wannabe boiled-frog crusader, this will be my final mention of OR's branding dilemma.)

Lohr argues that improvement in the performance of software such as
optimization algorithms has outpaced highly celebrated hardware speedups:

The rapid improvement in chips [...] has its own "law" -- Moore's Law, named
after the Intel co-founder Gordon Moore, who in 1965 predicted that the density
of transistors on integrated circuits would double every 18 months or
so...

... a study of progress over a 15-year span on a benchmark production-planning
task. Over that time, the speed of completing the calculations improved by a
factor of 43 million. Of the total, a factor of roughly 1,000 was attributable
to faster processor speeds, according to the research by Martin Grotschel, a
German scientist and mathematician. Yet a factor of 43,000 was due to
improvements in the efficiency of software algorithms...

But the ingenuity that computer scientists have put into algorithms have
yielded performance improvements that make even the exponential gains of Moore's
Law look trivial," said Edward Lazowska, a professor at the University of
Washington.

My first reaction was: These don't look like Martin's results.

I have since verified my hunch via e-mail: Martin was reporting the work of his
longtime associate Bob Bixby, who
has advanced a more calibrated version of Lohr's argument for more than 10
years. Indeed, the performance improvement for linear optimization software has
been nothing short of spectacular. Lohr's is the first recognition of this
revolution that I have read in the popular press.

(To put my views in context, I did my graduate work with Bob. Years
later, we also worked for the same company. However, I don't write numerical
software, and I played no direct role in the results being discussed.)

Lohr mentions production planning. Such problems, technically known as
mixed-integer programs, are complex variants of the steak grilling example I previously
described. To get a flavor of this complexity, instead of a backyard grill,
imagine an airline food-service operation that needs to turn out thousands of
steak and vegetable entrees. Naturally, for such a large-scale commercial
operation, lots of different grills with different capabilities are used. One
grill may cook up to five steaks or 20 servings of vegetables, or any smaller
combination that fits, at a time. Another may allow 12 steaks or 42 servings of
vegetables, or any smaller combination. And so on. Multiple cooks staff the
kitchen. Our challenge is to find a best possible sequence of grilling
operations.

Recall that for our example we sequenced six operations -- three
steaks with two sides per steak. For instance, our best possible sequence was
[Steak1.side1, Steak2.side1, Steak1.side2, Steak3.side1, Steak2.side2,
Steak3.side]. That yields -- you can work it out manually -- 11 meaningful cooking
sequences from which to pick the fastest.

Now, depending on the specifics, the number of possible cooking sequences in
a commercial kitchen -- the mathematician Paul
Halmos once said at a similar point in his exposition, "we are now waving
our hands" -- number in the billions. We cannot count our way out of
combinatorial explosion. Such problems are often modeled as mixed-integer
programs.

For Bob's representative test-set, the overall speedup was roughly 30
million-fold (not the 43 million in the extract above.) Think about that for a
minute. A computation process that -- on 15-year-old technology -- would have
taken a year to complete now takes one second. Bob's analysis showed that
hardware improvements only accounted for a 1,000-fold speedup. Algorithmic
improvements were responsible for the remaining 30,000-fold speedup.

How did it happen? How could algorithms improve so dramatically? The short
answer: Bob and his colleagues combed through nearly 50 years of research in
operations research and computer science. The mathematics was painstakingly
tested; what looks clever on paper doesn't always pan out in practice. The
techniques that tested best for speed and robustness (it is not uncommon for
numerical codes to crash) made it into software.

Much of the research used came from U.S. universities. Contributions also
arrived from academics such as Martin Groschel and his associates all over
Europe, and yet others in Canada, Japan and elsewhere. Finally, commercial
competition -- IBM Research was an early competitor but companies based in the UK
and Scandinavia also figure in the story -- kept up the pressure.

Linear optimization codes usually work their magic hidden under many layers
of enabling software -- databases, process workflows and business rules, a user
interface, etc. Booking a family vacation online is a perfect example. Clicking
on "Search" sets in motion a comparison of hundreds of thousands of itineraries
involving air transportation, hotel reservations, car rentals, and tickets to
child-friendly attractions. Optimization is critical, but it's only one step in
a multi-step process. Even if the optimization module speeds up tenfold, the
user experience improves only on the margin. Impressive as they are, the
improvements should not be extrapolated, either to all optimization problems, or
to all software. To that extent, Lohr's insight is less sensational than his
title suggests.

Let me conclude with three observations:

Without taking anything away from computational savants like Bob, this
success rests on a foundation of publicly funded research going back to the
fifties and sixties. Basic research remains the key to progress in technology
and business.

At least at the level of a sub-field, innovation is difficult to plan for or
predict. In 1991, linear programming was thought to be a mature field. From 1991
through 1998, linear programming performance improved dramatically. But
mixed-integer programming (its variant) remained difficult. Following a
tectonic performance jump in 1998, mixed-integer programming also began to be
considered practically tractable. No external pivotal event occurred in 1998;
success came "overnight" due to sustained long-term effort.

Branding often provides limited stickiness in niche software markets. For
optimization software in particular, switching costs can be low. It's easy to
benchmark performance, so businesses quickly switch to whatever gives them the
edge. Tall marketing claims are rarely left unchallenged. Vendor-promised
benchmarks are routinely tested and validated (or thrown out). The scientific
temper of operations research creates a near-ideal competitive landscape. The
progress should be attributed to a combination of openness and scientific
skepticism.

Sanjay Saigal is founder and CEO of Mudrika Education, Inc., with offices in Silicon Valley, CA and Delhi, India.

James Fallows is a national correspondent for The Atlantic and has written for the magazine since the late 1970s. He has reported extensively from outside the United States and once worked as President Carter's chief speechwriter. His latest book is China Airborne.
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James Fallows is based in Washington as a national correspondent for The Atlantic. He has worked for the magazine for nearly 30 years and in that time has also lived in Seattle, Berkeley, Austin, Tokyo, Kuala Lumpur, Shanghai, and Beijing. He was raised in Redlands, California, received his undergraduate degree in American history and literature from Harvard, and received a graduate degree in economics from Oxford as a Rhodes scholar. In addition to working for The Atlantic, he has spent two years as chief White House speechwriter for Jimmy Carter, two years as the editor of US News & World Report, and six months as a program designer at Microsoft. He is an instrument-rated private pilot. He is also now the chair in U.S. media at the U.S. Studies Centre at the University of Sydney, in Australia.

Fallows has been a finalist for the National Magazine Award five times and has won once; he has also won the American Book Award for nonfiction and a N.Y. Emmy award for the documentary series Doing Business in China. He was the founding chairman of the New America Foundation. His recent books Blind Into Baghdad (2006) and Postcards From Tomorrow Square (2009) are based on his writings for The Atlantic. His latest book is China Airborne. He is married to Deborah Fallows, author of the recent book Dreaming in Chinese. They have two married sons.

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